The life of a battery used in a cardiac pacemaker is assumed to be normally distributed. A random sample of 10 batteries is subject to an accelerated life test by running them continuously at an elevated temperature until failure, and the following lives are obtained.25.5, 26.1, 26.8, 23.2, 24.2, 28.4, 25.0, 27.8, 27.3, 25.7 (hour).a) Construct a 95% two-sided confidence interval on mean life in the accelerated test.(i) What is the lower value of the two-sided confidence interval? (ii) What is the higher value of the two-sided confidence interval?b) Construct a 99% lower one-sided confidence interval on mean battery life.c) Why would the manufacturer be interested in a one-sided confidence interval? Each question (indexed by Arabic number, e.g., Q1, Q2,...) may have multiple sub-questions (indexed bylower case alphabet, e.g., a, b, ..). To provide maximum partial credits, such question/sub-question isbroken down into many sequential questions. Such small questions are indexed by the Roman countingmethod with lower cases: i, ii, ...Q1. The life of a battery used in a cardiac pacemaker is assumed to be normally distributed. Arandom sample of 10 batteries is subject to an accelerated life test by running them continuously atan elevated temperature until failure, and the following lives are obtained.25.5, 26.1, 26.8, 23.2, 24.2, 28.4, 25.0, 27.8, 27.3, 25.7 (hour).a) Construct a 95% two-sided confidence interval on mean life in the accelerated test.(i) What is the lower value of the two-sided confidence interval?(ii) What is the higher value of the two-sided confidence interval?b) Construct a 99% lower one-sided confidence interval on mean battery life.c) Why would the manufacturer be interested in a one-sided confidence interval?

Random sample of 10 batteries given : n= 10 We have to calculate 95% confidence interval for two…

Answered: Each question (indexed by Arabic…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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The life of a battery used in a cardiac pacemaker is assumed to be normally distributed. A random sample of 10 batteries is subject to an accelerated life test by running them continuously at an elevated temperature until failure, and the following lives are obtained. 25.5, 26.1, 26.8, 23.2, 24.2, 28.4, 25.0, 27.8, 27.3, 25.7 (hour). a) Construct a 95% two-sided confidence interval on mean life in the accelerated test. (i) What is the lower value of the two-sided confidence interval? (ii) What is the higher value of the two-sided confidence interval? b) Construct a 99% lower one-sided confidence interval on mean battery life. c) Why would the manufacturer be interested in a one-sided confidence interval?

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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